The proof of the theorem above can be done by utilizing the fact that the operator \(a(\cdot ,\cdot )_\Omega \)  is coercive, \(b(\cdot ,\cdot )_\Omega \)  satisfies the inf-sup condition [1]}, and that the right hand side of the first equation of (REF ) can be seen as an action of an element of \(\operatorname{\mathbf {H}}^{-1}(\Omega )\) .
